Collocation approximations for weakly singular Volterra integro‐differential equations
A piecewise polynomial collocation method for solving linear weakly singular integro‐differential equations of Volterra type is constructed. The attainable order of convergence of collocation approximations on arbitrary and quasi‐uniform grids is studied theoretically and numerically. Silpnai sin...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2003-12-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/9787 |
| _version_ | 1818385757235052544 |
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| author | I. Parts A. Pedas |
| author_facet | I. Parts A. Pedas |
| author_sort | I. Parts |
| collection | DOAJ |
| description | A piecewise polynomial collocation method for solving linear weakly singular integro‐differential equations of Volterra type is constructed. The attainable order of convergence of collocation approximations on arbitrary and quasi‐uniform grids is studied theoretically and numerically.
Silpnai singuliarių Voltero integralinių-diferencialinių lygčių aproksimavimas kolokacijų metodu
Santrauka
Darbe nagrinejamas silpnai singuliariu Voltero integraliniu‐diferencialiniu lygčiu skaitinio artinio radimo algoritmas. Integralai priklauso ne tik nuo sprendinio, bet ir nuo jo pirmosios išvestines. Ištirtas kolokaciju metodo tikslumas, kai naudojami netolygūs ir artimi tolygiems tinklai. Teoriniai iverčiai patvirtinti skaičiavimo eksperimento rezultatais.
First Published Online: 14 Oct 2010 |
| first_indexed | 2024-12-14T03:43:13Z |
| format | Article |
| id | doaj.art-a52dc6feb2584a1a96bf26bec5c83ce3 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T03:43:13Z |
| publishDate | 2003-12-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-a52dc6feb2584a1a96bf26bec5c83ce32022-12-21T23:18:26ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102003-12-018410.3846/13926292.2003.9637233Collocation approximations for weakly singular Volterra integro‐differential equationsI. Parts0A. Pedas1Institute of Applied Mathematics , Liivi 2, Tartu, 50409, EstoniaInstitute of Applied Mathematics , Liivi 2, Tartu, 50409, EstoniaA piecewise polynomial collocation method for solving linear weakly singular integro‐differential equations of Volterra type is constructed. The attainable order of convergence of collocation approximations on arbitrary and quasi‐uniform grids is studied theoretically and numerically. Silpnai singuliarių Voltero integralinių-diferencialinių lygčių aproksimavimas kolokacijų metodu Santrauka Darbe nagrinejamas silpnai singuliariu Voltero integraliniu‐diferencialiniu lygčiu skaitinio artinio radimo algoritmas. Integralai priklauso ne tik nuo sprendinio, bet ir nuo jo pirmosios išvestines. Ištirtas kolokaciju metodo tikslumas, kai naudojami netolygūs ir artimi tolygiems tinklai. Teoriniai iverčiai patvirtinti skaičiavimo eksperimento rezultatais. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/9787Weakly singular Volterra integro‐differential equationpiecewise polynomial collocation methodorder of convergence |
| spellingShingle | I. Parts A. Pedas Collocation approximations for weakly singular Volterra integro‐differential equations Mathematical Modelling and Analysis Weakly singular Volterra integro‐differential equation piecewise polynomial collocation method order of convergence |
| title | Collocation approximations for weakly singular Volterra integro‐differential equations |
| title_full | Collocation approximations for weakly singular Volterra integro‐differential equations |
| title_fullStr | Collocation approximations for weakly singular Volterra integro‐differential equations |
| title_full_unstemmed | Collocation approximations for weakly singular Volterra integro‐differential equations |
| title_short | Collocation approximations for weakly singular Volterra integro‐differential equations |
| title_sort | collocation approximations for weakly singular volterra integro differential equations |
| topic | Weakly singular Volterra integro‐differential equation piecewise polynomial collocation method order of convergence |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/9787 |
| work_keys_str_mv | AT iparts collocationapproximationsforweaklysingularvolterraintegrodifferentialequations AT apedas collocationapproximationsforweaklysingularvolterraintegrodifferentialequations |